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S2 mistakes?

The question:

''The discrete random variable X takes integer values and is to be approximated by a normal distribution. Apply a continuity correction to the probabilities:

Answers:


a) Shouldn't the right-hand side be P(Y<7.5) rather than P(X≤7.5)?
b) Shouldn't the right-hand side be P(Y<9.5) rather than P(X≤9.5)?

Shouldn't all the right hand-sides have a Y instead of an X (since the continuity correction has been applied)?

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a) Why isn't the approximation Y~N(λ,λ) so Y~N(30,30)
Also shouldn't P(X≤20) be approximately equal to P(Y<20.5) rather than P(Y≤20.5)?

b) Surely P(X>43) is approximately equal to P(Y≥43.5) rather than P(Y>43.5)?
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a.png80.6KB
Original post by GPODT
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For a continuous random variable P(X<a) = P(X<=a), and similarly >. So, it's not a problem as such, but for consistency they ought to use <=, or >= throughout.

And yes, Y~N(30,30), since the variance is 30.
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GPODT
OP
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Original post by ghostwalker
For a continuous random variable P(X<a) = P(X<=a), and similarly >. So, it's not a problem as such, but for consistency they ought to use <=, or >= throughout.

And yes, Y~N(30,30), since the variance is 30.


With ''<='' you mean ≤ right?

Thanks
Original post by GPODT
With ''<='' you mean ≤ right?

Thanks


Yep. ≤\leq

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